Posted: 24/06/2012 at 11:48
Are they large flowers? If so, they are probably Group 2 (early large flowered) and will produce a 2nd set of flowers later in the year. What you should do now is remove all of the seedheads by snipping them off just above a pair of leaves. The new shoots you are seeing will produce the 2nd crop of flowers and you can try and train this downwards to cover some of the bare areas. That same growth will produce the early flowers next year.
You only do the main pruning in early spring. If severe pruning is needed, you can cut them back to the lowest pair of buds on each main stem. Doing that will mean you will lose the early flowers for that year, but they will still produce flowers later in the year. If you do cut them back hard in spring (even to the ground if you can't find any buds on the lower parts of the stems), they will usually produce new shoots from below ground, effectively revitalising them. If you do that, give them a good feed and mulch with a few inches of compost to build the soil level up at the roots.
To be sure of what variety and group they are, is there any chance you could upload some photos? Other clematis groups might need a slightly different approach.